The Divisor of Selberg's Zeta Function for Kleinian Groups

The Selberg Trace Formula and Selberg Zeta-Function for Cofinite Kleinian Groups with Finite Dimensional Unitary Representations

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitary representations. We show that the presence of cuspidal elliptic elements sometimes adds ramification po...

The Selberg Trace Formula and Selberg Zeta-function for Cofinite Kleinian Groups with Finite-dimensional Unitary Representations

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitary representations. We show that the presence of cuspidal elliptic elements sometimes adds ramification po...

Analogues of the Artin Factorization Formula for the Automorphic Scattering Matrix and Selberg Zeta-function Associated to a Kleinian Group

For Kleinian groups acting on hyperbolic three-space, we prove factorization formulas for both the Selberg zeta-function and the automorphic scattering matrix. We extend results of Venkov and Zograf from Fuchsian groups, to Kleinian groups, and we give a proof that is simple and extendable to more general groups.

An Extension of the Thermodynamic Formalism Approach to Selberg's Zeta Function for General Modular Groups

The Thermodynamic Formalism Approach to Selberg's Zeta Function for Psl(2, Z)

Besides the classical approach to Selberg's zeta function for cofinite Fuchsian groups [S] through the trace formula [V] there has been developed recently another one based on the thermodynamic formalism [R2] applied to the dynamical zeta function of Smale and Ruelle [F] which for geodesic flows on surfaces of constant negative curvature (c.n.c.) is closely related to Selberg's function for the...